Introduction to symplectic topology:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2017
|
| Edition: | Third edition |
| Series: | Oxford graduate texts in mathematics
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 583-610 |
| Physical Description: | xi, 623 Seiten Illustrationen |
| ISBN: | 9780198794905 9780198794899 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Introduction to symplectic topology
Autor: McDuff, Dusa
Jahr: 2017
CONTENTS
Introduction 1
I FOUNDATIONS
1 From classical to modern 11
1.1 Hamiltonian mechanics 11
1.2 The symplectic topology of Euclidean space 28
2 Linear symplectic geometry 37
2.1 Symplectic vector spaces 38
2.2 The symplectic linear group 43
2.3 Lagrangian subspaces 50
2.4 The affine nonsqueezing theorem 55
2.5 Linear complex structures 61
2.6 Symplectic vector bundles 79
2.7 First Chern class 85
3 Symplectic manifolds 94
3.1 Basic concepts 94
3.2 Moser isotopy and Darboux s theorem 108
3.3 Isotopy extension theorems 112
3.4 Submanifolds of symplectic manifolds 116
3.5 Contact structures 125
4 Almost complex structures 152
4.1 Almost complex structures 153
4.2 Integrability 161
4.3 Kahler manifolds 167
4.4 Kähler surfaces 172
4.5 J-holomorphic curves 180
II SYMPLECTIC MANIFOLDS
5 Symplectic group actions 191
5.1 Circle actions 192
5.2 Moment maps 202
5.3 Examples 207
5.4 Symplectic quotients 218
5.5 Convexity 229
5.6 Localization 240
5.7 Remarks on GIT 246
X
Contents
6 Symplectic Fibrations 252
6.1 Symplectic fibrations 252
6.2 Symplectic 2-sphere bundles 257
6.3 Symplectic connections 262
6.4 Hamiltonian holonomy and the coupling form 271
6.5 Hamiltonian fibrations 282
7 Constructing Symplectic Manifolds 289
7.1 Blowing up and down 289
7.2 Connected sums 316
7.3 The telescope construction 322
7.4 Donaldson submanifolds 328
III SYMPLECTOMORPHISMS
8 Area-preserving diffeomorphisms 341
8.1 Periodic orbits 341
8.2 The Poincare-Birkhoff theorem 344
8.3 The billiard problem 350
9 Generating functions 356
9.1 Generating functions and symplectic action 356
9.2 Discrete Hamiltonian mechanics 363
9.3 Hamiltonian symplectomorphisms 369
9.4 Lagrangian submanifolds 378
10 The group of symplectomorphisms 385
10.1 Basic properties 385
10.2 The flux homomorphism 390
10.3 The Calabi homomorphism 406
10.4 The topology of symplectomorphism groups 411
IV SYMPLECTIC INVARIANTS
11 The Arnold conjecture 417
11.1 Symplectic fixed points 418
11.2 Morse theory and the Conley index 425
11.3 Lagrangian intersections 435
11.4 Floer homology 446
12 Symplectic capacities 457
12.1 Nonsqueezing and capacities 457
12.2 Rigidity 462
12.3 The Hofer metric 465
12.4 The Hofer-Zehnder capacity 481
12.5 A variational argument 489
Contents xi
13 Questions of existence and uniqueness 503
13.1 Existence and uniqueness of symplectic structures 503
13.2 Examples 507
13.3 Taubes-Seiberg-Witten theory 516
13.4 Symplectic four-manifolds 533
14 Open problems 549
14.1 Symplectic structures 549
14.2 Symplectomorphisms 553
14.3 Lagrangian submanifolds and cotangent bundles 558
14.4 Fano manifolds 562
14.5 Donaldson hypersurfaces 563
14.6 Contact geometry 565
14.7 Continuous symplectic topology 567
14.8 Symplectic embeddings 569
14.9 Symplectic topology of Euclidean space 571
A Smooth maps 574
A.l Smooth functions on manifolds with corners 574
A.2 Extension 578
A.3 Construction of a smooth function 580
References 583
Index
611
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| any_adam_object | 1 |
| author | McDuff, Dusa 1945- Salamon, Dietmar 1953- |
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| classification_rvk | SK 350 |
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| ctrlnum | (OCoLC)990095497 (DE-599)BSZ483400149 |
| discipline | Mathematik |
| edition | Third edition |
| format | Book |
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| institution | BVB |
| isbn | 9780198794905 9780198794899 |
| language | English |
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| spelling | McDuff, Dusa 1945- (DE-588)172795176 aut Introduction to symplectic topology Dusa McDuff (Professor of mathematics, Barnard College, Columbia University) ; Dietmar Salamon (Professor of mathematics, ETH Zürich) Third edition Oxford Oxford University Press 2017 xi, 623 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 27 Literaturverzeichnis Seite 583-610 Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Symplektische Abbildung (DE-588)4332207-4 gnd rswk-swf Symplektische Invariante (DE-588)4350963-0 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 s DE-604 Symplektische Abbildung (DE-588)4332207-4 s Symplektische Invariante (DE-588)4350963-0 s Symplektische Mannigfaltigkeit (DE-588)4290704-4 s 1\p DE-604 Salamon, Dietmar 1953- (DE-588)1015895271 aut Oxford graduate texts in mathematics 27 (DE-604)BV011416591 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029640628&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McDuff, Dusa 1945- Salamon, Dietmar 1953- Introduction to symplectic topology Oxford graduate texts in mathematics Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Symplektische Abbildung (DE-588)4332207-4 gnd Symplektische Invariante (DE-588)4350963-0 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4290704-4 (DE-588)4332207-4 (DE-588)4350963-0 (DE-588)4194232-2 |
| title | Introduction to symplectic topology |
| title_auth | Introduction to symplectic topology |
| title_exact_search | Introduction to symplectic topology |
| title_full | Introduction to symplectic topology Dusa McDuff (Professor of mathematics, Barnard College, Columbia University) ; Dietmar Salamon (Professor of mathematics, ETH Zürich) |
| title_fullStr | Introduction to symplectic topology Dusa McDuff (Professor of mathematics, Barnard College, Columbia University) ; Dietmar Salamon (Professor of mathematics, ETH Zürich) |
| title_full_unstemmed | Introduction to symplectic topology Dusa McDuff (Professor of mathematics, Barnard College, Columbia University) ; Dietmar Salamon (Professor of mathematics, ETH Zürich) |
| title_short | Introduction to symplectic topology |
| title_sort | introduction to symplectic topology |
| topic | Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Symplektische Abbildung (DE-588)4332207-4 gnd Symplektische Invariante (DE-588)4350963-0 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Symplektische Mannigfaltigkeit Symplektische Abbildung Symplektische Invariante Symplektische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029640628&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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